#35212922

order	20864
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	Q₈⋊C₈×C₁₆₃ ⋊ C₂
Sylow	C₁₆₃ ⋊ #1477

264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 10432

Polycyclic presentation:

2^7,163|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cf,d^b=df,h^b=h^162,h^c=h^162

2312 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 2896);